Organic fabrics are grown naturally without the use of pesticides. A certified organic fabric is one that has been manufactured according to strict guidelines to ensure that it is as it claims to be. These certified organics are usually referenced with an agency that has given the certification (such as SKAL or Demeter)
Some fabrics are a blend of organic and non-organic fibres. They are most often found unbleached, but are occasionally "low impact" bleached, dyed or printed. Dying or bleaching an organic fabric generally stops it being classed as an organic fabric, however some "low-impact" dyes can be used on organic fabrics to colour them in the least environmentally damaging/least chemical way possible. Depending on the way it was done (if this was done during manufacture), it may still keep it's certified status.
Bamboo & organic cotton fleece can come in an 85% bamboo, 15% organic cotton ratio.